Introduction to instanton knot homology

Floer theory is an infinite-dimensional version of Morse theory and has provided powerful invariants in the study of low-dimensional topology. In the context of Yang-Mills gauge theory, some versions of Floer homology groups for knots have been developed. These knot invariants are called instanton knot homology groups and are strongly related to representations of the fundamental group of the knot complement.
In this talk, the speaker introduces basic constructions of instanton knot homology groups and recent developments related to the equivariant version of instanton knot homology theory.